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A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 56 (10 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Petri Nets And Step Transition Systems
 International Journal of Foundations of Computer Science
, 1992
"... Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step. Petri ne ..."
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Cited by 46 (1 self)
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Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step. Petri nets (or Place/Transition nets) give rise to such step transition systems in a natural way  the marking diagram of a Petri net is the canonical transition system associated with it. In this paper, we characterize the class of PNtransition systems, which are precisely those step transition systems generated by Petri nets. We express the correspondence between PNtransition systems and Petri nets in terms of an adjunction between a category of PNtransition systems and a category of Petri nets in which the associated morphisms are behaviourpreserving in a strong and natural sense.
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
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Cited by 42 (3 self)
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This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
ZeroSafe Nets: Comparing the Collective and Individual Token Approaches
"... The main feature of zerosafe nets is a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable places, zerosafe nets are equipped with zero places, which in an observable marking cannot contain any token. This yields the notion of transaction: a basic ..."
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Cited by 39 (20 self)
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The main feature of zerosafe nets is a primitive notion of transition synchronization. To this aim, besides ordinary places, called stable places, zerosafe nets are equipped with zero places, which in an observable marking cannot contain any token. This yields the notion of transaction: a basic atomic computation, which may use zero tokens as triggers, but defines an evolution between observable markings only. The abstract counterpart of a generic zerosafe net B consists of an ordinary P/T net whose places are the stable places of B, and whose transitions represent the transactions of B. The two nets offer both the refined and the abstract model of the same system, where the former can be much smaller than the latter, because of the transition synchronization mechanism. Depending on the chosen approach  collective vs individual token philosophy  two notions of transaction may be defined, each leading to different operational and abstract models. Their comparison is fully dis...
Chu spaces and their interpretation as concurrent objects
, 2005
"... A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of pa ..."
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A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which takes A to be a schedule of events distributed in time, X to be an automaton of states forming an information system in the sense of Scott, and the pairs (a, x) in the =  relation to be the individual transcriptions of the making of history. The traditional homogeneous binary relations of transition on X and precedence on A are recovered as respectively the right and left residuals of the heterogeneous binary relation =  with itself. The natural algebra of Chu spaces is that of linear logic, made a process algebra by the process interpretation.
On the Semantics of Place/Transition Petri Nets
, 1992
"... Abstract. In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical “token game”, one can model the behaviour of Petri nets via nonsequential processes, via unfolding constructions, which provide formal relationships between nets an ..."
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Abstract. In the last few years, the semantics of Petri nets has been investigated in several different ways. Apart from the classical “token game”, one can model the behaviour of Petri nets via nonsequential processes, via unfolding constructions, which provide formal relationships between nets and domains, and via algebraic models, which view Petri nets as essentially algebraic theories whose models are monoidal categories. In this paper we show that these three points of view can be reconciled. More precisely, we introduce the new notion of decorated processes of Petri nets and we show that they induce on nets the same semantics as that of unfolding. In addition, we prove that the decorated processes of a net N can be axiomatized as the arrows of a symmetric monoidal category which, therefore, provides the aforesaid unification.
Higher Dimensional Automata Revisited
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2000
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Relating StateBased and ProcessBased Concurrency through Linear Logic
, 2006
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired to Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic. In the second part of the paper, we propose a completely new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous πcalculus to rewrite operators, while the structural equivalence corresponds directly to logicallymotivated structural properties of ωmultisets (with one exception).